Thermodynamical hairs of the four-dimensional Taub-Newman-Unti-Tamburino spacetimes

TL;DR

This paper reveals that four-dimensional Taub-NUT spacetimes possess multiple thermodynamic hairs, including mass, angular momentum, gravitomagnetic charge, and dual mass, redefining the understanding of NUT charge in black hole thermodynamics.

Contribution

It introduces a systematic method to analyze the thermodynamics of NUT-charged spacetimes, demonstrating the NUT charge as a multihair with multiple physical features.

Findings

NUT charge acts as a multihair with rotation and electromagnetic characteristics.

Restoration of the Bekenstein-Hawking entropy relation without constraints.

Clarification of the NUT parameter's physical meaning in thermodynamics.

Abstract

It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass ($M = m$), the "angular momentum" ($J_n = mn$), the gravitomagnetic charge ($N = n$), and/or the dual (magnetic) mass ($\widetilde{M} = n$). In other words, the NUT charge is a thermodynamic multihair which means that it simultaneously has both rotation-like and electromagnetic charge-like characteristics; this is in sharp contrast with the previous knowledge that it has only one physical feature, or that it is purely a single solution parameter. To arrive at this novel result, we put forward a simple, systematic way to investigate the consistent thermodynamic first law and Bekenstein-Smarr mass formulas of all four-dimensional spacetimes that contain a nonzero NUT charge, facilitated by first deriving a meaningful Christodoulou-Ruffini-type squared-mass formula. In this way, not only can the elegant Bekenstein-Hawking one-quarter area-entropy relation be naturally restored in the Lorentzian and Euclidian sectors of generic Taub-NUT-type spacetimes without imposing any constraint condition, but also the physical meaning of the NUT parameter as a poly-facet can be completely clarified in the thermodynamic sense for the first time.